@@ -28,35 +28,28 @@ jobs:
         cache-dependency-path: 'Doc/requirements.txt'
     - name: 'Install build dependencies'
       run: make -C Doc/ venv
-    - name: 'Build HTML documentation'
-      run: make -C Doc/ SPHINXOPTS="-q" SPHINXERRORHANDLING="-W --keep-going" html
 
-    # Add pull request annotations for Sphinx nitpicks (missing references)
+    # To annotate PRs with Sphinx nitpicks (missing references)
     - name: 'Get list of changed files'
       if: github.event_name == 'pull_request'
       id: changed_files
       uses: Ana06/get-changed-files@v2.2.0
       with:
         filter: "Doc/**"
         format: csv  # works for paths with spaces
-    - name: 'Build changed files in nit-picky mode'
-      if: github.event_name == 'pull_request'
+    - name: 'Build HTML documentation'
       continue-on-error: true
       run: |
         set -Eeuo pipefail
-        # Mark files the pull request modified
-        python Doc/tools/touch-clean-files.py --clean '${{ steps.changed_files.outputs.added_modified }}'
-        # Build docs with the '-n' (nit-picky) option; convert warnings to annotations
-        make -C Doc/ PYTHON=../python SPHINXOPTS="-q -n --keep-going" html 2>&1 |
-            python Doc/tools/warnings-to-gh-actions.py
-
-    # Ensure some files always pass Sphinx nit-picky mode (no missing references)
-    - name: 'Build known-good files in nit-picky mode'
+        # Build docs with the '-n' (nit-picky) option; write warnings to file
+        make -C Doc/ PYTHON=../python SPHINXOPTS="-q -n -W --keep-going -w sphinx-warnings.txt" html
+    - name: 'Check warnings'
+      if: github.event_name == 'pull_request'
       run: |
-        # Mark files that must pass nit-picky
-        python Doc/tools/touch-clean-files.py
-        # Build docs with the '-n' (nit-picky) option, convert warnings to errors (-W)
-        make -C Doc/ PYTHON=../python SPHINXOPTS="-q -n -W --keep-going" html 2>&1
+        python Doc/tools/check-warnings.py \
+          --check-and-annotate '${{ steps.changed_files.outputs.added_modified }}' \
+          --fail-if-regression \
+          --fail-if-improved
 
   # This build doesn't use problem matchers or check annotations
   build_doc_oldest_supported_sphinx:
 
@@ -10,7 +10,7 @@ repos:
         types_or: [c, python, rst]
 
   - repo: https://github.com/sphinx-contrib/sphinx-lint
-    rev: v0.6.7
+    rev: v0.6.8
     hooks:
       - id: sphinx-lint
         args: [--enable=default-role]
 
@@ -555,7 +555,7 @@ Building values
       Same as ``s#``.
 
    ``u`` (:class:`str`) [const wchar_t \*]
-      Convert a null-terminated :c:expr:`wchar_t` buffer of Unicode (UTF-16 or UCS-4)
+      Convert a null-terminated :c:type:`wchar_t` buffer of Unicode (UTF-16 or UCS-4)
       data to a Python Unicode object.  If the Unicode buffer pointer is ``NULL``,
       ``None`` is returned.
 
 
@@ -225,7 +225,7 @@ object via :c:func:`PyObject_GetBuffer`. Since the complexity of the logical
 structure of the memory can vary drastically, the consumer uses the *flags*
 argument to specify the exact buffer type it can handle.
 
-All :c:data:`Py_buffer` fields are unambiguously defined by the request
+All :c:type:`Py_buffer` fields are unambiguously defined by the request
 type.
 
 request-independent fields
@@ -464,7 +464,7 @@ Buffer-related functions
 
 .. c:function:: Py_ssize_t PyBuffer_SizeFromFormat(const char *format)
 
-   Return the implied :c:data:`~Py_buffer.itemsize` from :c:data:`~Py_buffer.format`.
+   Return the implied :c:member:`~Py_buffer.itemsize` from :c:member:`~Py_buffer.format`.
    On error, raise an exception and return -1.
 
    .. versionadded:: 3.9
 
@@ -152,7 +152,7 @@ Vectorcall Support API
    This is mostly useful to check whether or not *op* supports vectorcall,
    which can be done by checking ``PyVectorcall_Function(op) != NULL``.
 
-   .. versionadded:: 3.8
+   .. versionadded:: 3.9
 
 .. c:function:: PyObject* PyVectorcall_Call(PyObject *callable, PyObject *tuple, PyObject *dict)
 
 
@@ -163,7 +163,7 @@ For convenience, some of these functions will always return a
    This is a convenience function to raise an exception when a C library function
    has returned an error and set the C variable :c:data:`errno`.  It constructs a
    tuple object whose first item is the integer :c:data:`errno` value and whose
-   second item is the corresponding error message (gotten from :c:func:`strerror`),
+   second item is the corresponding error message (gotten from :c:func:`!strerror`),
    and then calls ``PyErr_SetObject(type, object)``.  On Unix, when the
    :c:data:`errno` value is :c:macro:`EINTR`, indicating an interrupted system call,
    this calls :c:func:`PyErr_CheckSignals`, and if that set the error indicator,
 
@@ -6,7 +6,7 @@ Iterator Objects
 ----------------
 
 Python provides two general-purpose iterator objects.  The first, a sequence
-iterator, works with an arbitrary sequence supporting the :meth:`__getitem__`
+iterator, works with an arbitrary sequence supporting the :meth:`~object.__getitem__`
 method.  The second works with a callable object and a sentinel value, calling
 the callable for each item in the sequence, and ending the iteration when the
 sentinel value is returned.
 
@@ -13,7 +13,7 @@ See also :c:func:`PyObject_GetItem`, :c:func:`PyObject_SetItem` and
 
    Return ``1`` if the object provides the mapping protocol or supports slicing,
    and ``0`` otherwise.  Note that it returns ``1`` for Python classes with
-   a :meth:`__getitem__` method, since in general it is impossible to
+   a :meth:`~object.__getitem__` method, since in general it is impossible to
    determine what type of keys the class supports. This function always succeeds.
 
 
@@ -90,7 +90,7 @@ See also :c:func:`PyObject_GetItem`, :c:func:`PyObject_SetItem` and
    This is equivalent to the Python expression ``key in o``.
    This function always succeeds.
 
-   Note that exceptions which occur while calling the :meth:`__getitem__`
+   Note that exceptions which occur while calling the :meth:`~object.__getitem__`
    method will get suppressed.
    To get error reporting use :c:func:`PyObject_GetItem()` instead.
 
@@ -101,7 +101,7 @@ See also :c:func:`PyObject_GetItem`, :c:func:`PyObject_SetItem` and
    This is equivalent to the Python expression ``key in o``.
    This function always succeeds.
 
-   Note that exceptions which occur while calling the :meth:`__getitem__`
+   Note that exceptions which occur while calling the :meth:`~object.__getitem__`
    method and creating a temporary string object will get suppressed.
    To get error reporting use :c:func:`PyMapping_GetItemString()` instead.
 
 
@@ -581,7 +581,7 @@ that the treatment of negative indices differs from a Python slice):
     default).
 
     A serial number, incremented by 1 on each call to a malloc-like or
-    realloc-like function.  Big-endian ``size_t``.  If "bad memory" is detected
+    realloc-like function.  Big-endian :c:type:`size_t`.  If "bad memory" is detected
     later, the serial number gives an excellent way to set a breakpoint on the
     next run, to capture the instant at which this block was passed out.  The
     static function bumpserialno() in obmalloc.c is the only place the serial
 
@@ -7,8 +7,8 @@ Instance Method Objects
 
 .. index:: pair: object; instancemethod
 
-An instance method is a wrapper for a :c:data:`PyCFunction` and the new way
-to bind a :c:data:`PyCFunction` to a class object. It replaces the former call
+An instance method is a wrapper for a :c:type:`PyCFunction` and the new way
+to bind a :c:type:`PyCFunction` to a class object. It replaces the former call
 ``PyMethod_New(func, NULL, class)``.